6.GR.1 Lesson 5-9-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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5.9 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

Area of Regular Polygons · Regular Polygon · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do we find the area of a regular polygon?
1A regular polygon splits into the same number of triangles as it has sides, so total area = (one triangle's area) × (number of sides).
  • A regular polygon is a closed shape with straight sides where every side is the same length and every angle is the same size. We can decompose it (break it apart) into equal triangles from the center, then add up their areas. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. My hexagon has 6 equal sides. Each side is 6 feet, and each center triangle has a height of 5.2 feet.
  2. First I find one triangle: A = ½ × base × height = ½ × 6 × 5.2.
  3. I multiply: 6 × 5.2 = 31.2, then ½ × 31.2 = 15.6 square feet.
  4. A hexagon has 6 sides, so it has 6 equal triangles.
  5. I multiply: 6 × 15.6 = 93.6. So the total area is 93.6 square feet.
3Mathematical Word Bank
  • Area of Regular Polygons (Área de polígonos regulares) — The space a regular polygon covers. Split it from the center into identical triangles, find one triangle's area, then multiply by how many there are.
  • Regular Polygon (Polígono regular) — A closed flat shape made of straight sides, where every side is the same length and every angle is the same size.
  • Decompose (Descomponer) — To break a shape into smaller, simpler shapes.
  • Triangle (Triángulo) — A shape with three sides.
  • Composite (Compuesto) — Made by putting two or more simple shapes together.
  • Formula (Fórmula) — A math rule written with symbols.
4Watch out
  • A common mistake in Area of Regular Polygons is stopping after finding the area of ONE triangle and reporting that as the total area — or adding the number of triangles instead of multiplying. Remember: total area = (one triangle's area) × (number of sides), not (one triangle's area) + (number of sides).
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Each regular polygon below is cut into congruent triangles by drawing a line from the center to every corner. Sort by how many triangles it makes.

    Target Categories: More than 5 triangles 5 or fewer triangles
    • 2 FILL TABLE

      Solve the mathematical problem. Show all of your work and reasoning.

      PolygonNumber of TrianglesTriangle BaseTriangle HeightArea of One TriangleTotal Area
      Hexagon
      Pentagon
      Square
      Octagon
      ✏️ Scratchpad / Reasoning
    SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
    1. 3 MULTIPLE CHOICE

      A regular hexagon is divided into 6 equal triangles from the center. Each triangle has a base of 6 ft and a height of 5.2 ft. What is the area of one triangle?

      1. A15.6 sq ft
      2. B31.2 sq ft
      3. C11.2 sq ft
      4. D15.6 ft
      Formula
      Put the numbers in
      Work it out
      Answer with its unit
      1. 1Name itWhich measure is asked?
      2. 2Write the formulaBefore any numbers.
      3. 3SubstituteMatch each letter.
      4. 4Unitunits, sq units, or cubic?
    2. 4 MULTIPLE CHOICE

      Using the triangle from the previous question, what is the total area of the hexagonal skylight?

      1. A93.6 sq ft
      2. B15.6 sq ft
      3. C187.2 sq ft
      4. D62.4 sq ft
      Formula
      Put the numbers in
      Work it out
      Answer with its unit
      1. 1Name itWhich measure is asked?
      2. 2Write the formulaBefore any numbers.
      3. 3SubstituteMatch each letter.
      4. 4Unitunits, sq units, or cubic?
    3. 5 MULTIPLE CHOICE

      A regular hexagon is split into 6 triangles, each with base 4 cm and height 3.5 cm. What is the total area?

      1. A42 sq cm
      2. B21 sq cm
      3. C84 sq cm
      4. D14 sq cm
      Formula
      Put the numbers in
      Work it out
      Answer with its unit
      1. 1Name itWhich measure is asked?
      2. 2Write the formulaBefore any numbers.
      3. 3SubstituteMatch each letter.
      4. 4Unitunits, sq units, or cubic?
    4. 6 MULTIPLE CHOICE

      How many triangles can you make from the center of a regular pentagon?

      1. A5
      2. B3
      3. C6
      4. D10
      ✏️ Workspace & Solution Steps
    🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

    Group Discussion Prompt: How does your visual model justify your mathematical solution?

    🗣️ Partner A:
    Partner A: "I modeled this by identifying the relationship and..."
    👂 Partner B:
    Partner B: "I agree with your step because the standard mathematical rule states..."
    ✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

    Complete each sentence stem to demonstrate precise mathematical reasoning:

    BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.
    BUT An estimate provides a quick benchmark, but an exact proof is required for precision.
    SO The quantities follow the standard rule, so the final result is verified with certainty.
    📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

    Writing Task: Justify why your mathematical solution is accurate and complete.

    C Claim
    Starter: My mathematical claim is that the solution is...
    E Evidence
    Starter: The evidence from the model/table demonstrates that...
    R Reasoning
    Starter: This proves my answer because the standard mathematical definition of...
    Student Mastery Self-Assessment:
    1 · Need More Support
    2 · Getting Closer
    3 · Got It / Solid
    4 · Master / Can Teach It